"If you were in the LDS Church (Mormons) and I could prove to you that it was not a religion teaching the truth, would you listen and act on what I said, even though all your friends and family are Mormons ?"
That's a great approach to lead in with, and it may give you an entrance to introduce something that will impact that person emotionally, but you don't win them over with pure logic. You might be able to use logic to derive a conclusion that results in them wanting to leave, but it's only because this conclusion strikes at one of their core values.
The point of all this is not to say that there's no place for logic in trying to wake someone up (in spite of my rather sensationalist thread title). The point is that just using logic doesn't work unless you're able to convince someone of a fact that impacts them at a core emotional level enough to motivate action. I can prove to my wife that the cult has killed people unnecessarily and even get her to agree, but apparently that fact does not impact her on an emotional level enough to motivate action. She's more emotionally invested in the fantasy of paradise than she is in the realities of the current world and so death in this world does not seem to phase her.